Number String

给一个只含‘I','D','?'三种字符的字符串，I表示当前数字大于前面的数字，D表示当前的数字小于前面一位的数字，？表示当前位既可以小于又可以大于。

问1~n的排列中有多少个满足该字符串。

Sample Input

II
ID
DI
DD
?D
??

Sample Output

1
2
2
1
3
6

Hint

Permutation {1,2,3} has signature "II".
Permutations {1,3,2} and {2,3,1} have signature "ID".
Permutations {3,1,2} and {2,1,3} have signature "DI".
Permutation {3,2,1} has signature "DD".
"?D" can be either "ID" or "DD".
"??" gives all possible permutations of length 3.

#include <iostream>
#include <cmath>
#include <math.h>
#include <vector>
#include <cstdio>
#include <cstring>
#include <string>
#include <string.h>
#include <algorithm>
using namespace std;
#define ll long long
const int mod = 1000000007;
const int n = 1005;
ll sum[n][n];
int main()
{
    memset(sum,0,sizeof(sum));
    string s;
    sum[0][1] = 1;
    while(cin>>s)
    {
        for(int i=1;i<=s.size();i++)
        {
            for(int j=1;j<=i+1;j++)
            {
                sum[i][j] = sum[i][j-1];
                if(s[i-1] != 'D') sum[i][j] += sum[i-1][j-1];
                if(s[i-1] != 'I') sum[i][j] += sum[i-1][i] -sum[i-1][j-1]+mod;
                sum[i][j] %= mod;
            }
        }
        cout<<sum[ s.size() ][ s.size() + 1 ]<<endl;
    }
    return 0;
}